Chimamanda Ngozi Adichie's first novel, Purple Hibiscus, opened with a sentence that saluted Chinua Achebe's best-known novel, Things Fall Apart, by including the words of his title. It was a suitable echo: she writes in the tradition of Nigeria's great novelist. Purple Hibiscus was a portrait of a family tyrannised by a violent, religious despot of a father. It described, in particular, the unsentimental education of a teenage girl, as beautiful and crushable as a hibiscus flower. The book was disciplined and intense (it picked up the Commonwealth First Book prize and was shortlisted for the 2004 Orange Prize). The structure of the second is not so tight, but this works in its favour; it has a ramshackle freedom and exuberant ambition.

It opens modestly with a comic chapter narrated by Ugwu, a houseboy who longs to please. His only fault is that he tries too hard - he burns his master Odenigbo's socks by ironing them. But he doesn't burn his boats. Odenigbo, a broad-minded lecturer at the University of Nigeria in Nsukka, although vexed by the fate of his socks, does not sack the boy. He recognises that Ugwu is clever and deserves an education, for which he is prepared to pay. A charming, lasting relationship is about to begin.

But long before the end of the novel, the characters have committed more serious crimes than sock-singeing, Ugwu included. And the story loses altogether its peaceable lightness as the war between Biafra and Nigeria (1967-70) threatens to overwhelm it. Yet the narrative, extraordinarily given that Biafra is involved, remains warm and as full-figured as its curvy heroine, Olanna. No matter how dire the circumstances, censure is not Adichie's thing. She leaves the judging to us.

Every page is a sketch of Nigeria: cashew trees, mangoes, mud walls, cassava patches, nouveau riche ostentation (she sums up the conversation of such people in the single line: 'How's the new car behaving?'). She has a sure satirical edge. She delights, for example, in the image of Olanna's mother, married to a rich businessman, hiding her diamonds inside her bra. She sees with a loving but undeceived eye.

Adichie's strength lies in weakness: all her characters are disadvantaged by being themselves (there is no such thing as a fault-free human being). And she ingeniously uses their failings as a way of establishing narrative tension and of creating comedy. Ugwu does not know enough; Olanna, beautiful and educated, knows too much. When she visits her aunt and uncle, she is ashamed to feel discomfited by their poverty, tries not to mind the cockroach eggs, the smoke.

Richard, last of the trio of narrators, is wrong-footed by being white and British. He is good-hearted, talentless, ingratiating. He is obsessed with ancient Nigerian pots and fruitlessly attempts to write a novel with the hopeless title: In the Time of Roped Pots. I couldn't help wishing for a less anaemic sample of British manhood.

Adichie is concerned with what it means to belong in a country, to a family, with a lover. And belonging is never straightforward. The most arresting character in the book is Olanna's twin sister, Kainene. She is sharp, impenetrable and lacks her sister's voluptuous looks. Richard falls in love with her despite (or because of?) her asperity - she is frighteningly competent at putting him in his place. When he admires her necklace, she replies: 'Of course it is not lovely. My father has obscene taste in jewellery.'

But Kainene's hardness is superficial. And when the war starts, she throws herself into relief work. Reading this novel is as close as you can get to the terrifying experience of being at war. And there is no character, with the exception of Kainene and Olanna's parents, who have fled to London, whose life is not in danger. The description of starvation is so vivid that your heart (and stomach) ache. When Olanna queues for powdered egg for her sick baby daughter, you feel that you are in the crowd fighting with her. Adichie never writes like a reporter or a historian, although she has done her homework thoroughly. She never loses track of the personal. As well as freshly recreating this nightmarish chapter in her country's history, she explores survival within relationships. She writes about the pain of sexual infidelity and the slow process by which love, if strong enough, may overcome.

The novel is an immense achievement. The foreign becomes familiar, a distant war comes close, a particular story seems universal. Nothing is falling apart for Adichie: everything is coming together.